chore(i18n,learn): processed translations (#44851)
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---
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id: 5900f5061000cf542c510017
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title: 'Problem 409: Nim Extreme'
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challengeType: 5
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forumTopicId: 302077
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dashedName: problem-409-nim-extreme
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---
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# --description--
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Let $n$ be a positive integer. Consider nim positions where:
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- There are $n$ non-empty piles.
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- Each pile has size less than $2^n$.
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- No two piles have the same size.
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Let $W(n)$ be the number of winning nim positions satisfying the above conditions (a position is winning if the first player has a winning strategy).
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For example, $W(1) = 1$, $W(2) = 6$, $W(3) = 168$, $W(5) = 19\\,764\\,360$ and $W(100)\bmod 1\\,000\\,000\\,007 = 384\\,777\\,056$.
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Find $W(10\\,000\\,000)\bmod 1\\,000\\,000\\,007$.
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# --hints--
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`nimExtreme()` should return `253223948`.
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```js
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assert.strictEqual(nimExtreme(), 253223948);
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```
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# --seed--
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## --seed-contents--
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```js
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function nimExtreme() {
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return true;
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}
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nimExtreme();
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```
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# --solutions--
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```js
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// solution required
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```
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